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CHAPTER 12:PART 2
THE CONDITIONS OF
LINEAR MOTION
KINESIOLOGY
Scientific Basis of Human Motion, 12th edition
Hamilton, Weimar & Luttgens
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
Revised by Hamilton & Weimar
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Forces That Modify Motion
Weight
 The force of gravity is
measured as the weight of
the body applied through
the center of gravity of the
body and directed toward
the earth’s axis.
Weight
W = mg
Fig 12.16
12B-2
Contact Forces:
Normal Reaction
 For every action there is
an equal and opposite
reaction.
 The jumper pushes off the ground
and the ground pushes back.
Reaction
Fig 12.17
Action
12B-3
Contact Forces:
Friction
 Friction is the force that opposes
efforts to slide or roll one body over
another.
 In some cases we try to increase friction for a
more effective performance.
 In other cases we try to decrease friction for a
more effective performance.
 The amount of friction depends on the
nature of the surfaces and the forces
pressing them together.
12B-4
Friction
Friction is proportional to
the force pressing two
surfaces together.
 Force of friction acts
parallel to the surfaces
and opposite to the
direction of motion.
Fig 12.18
W = weight
T = reactive (normal) force
of table
P = force needed to move
F = force resisting motion
12B-5
Coefficient of friction, 
 The ratio of force needed to overcome the
friction, P, to the force holding the surface
together, W:
 = P / W or
 = Fmax/FN
 Large coefficient surfaces cling together.
 Small coefficient surfaces slide easily.
 Coefficient of 0.0 = frictionless surface.
12B-6
Coefficient of Friction
 May be found by:
 Placing one object on a second and tilt the
second until first begins to slide.
 The tangent of the angle with horizontal is
the coefficient of friction.
Fig 12.19
12B-7
Elasticity and Rebound
 Objects rebound in a predictable manner.
 The nature of rebound is governed by
elasticity, mass, and velocity of rebounding
surface, friction between surfaces, and
angle of contact.
 Elasticity is the ability to resist distorting
influences and to return to the original size
and shape.
12B-8
Elasticity and Rebound
 Stress is the force that
acts to distort.
 Strain is the distortion
that occurs.
 Stress may take the
form of tension,
compression, bending,
or torsion.
Fig 12.21b
12B-9
Coefficient of Elasticity
 Is defined as the stress divided by the strain.
 Most commonly determined in the
compression of balls by comparing drop
height with the bounce height.
e=
bounce height
drop height
 The closer to 1.0 the more perfect the
elasticity.
12B-10
Coefficient of Elasticity
 Also may be found using the Law of
Conservation of Momentum:
 Using the change in velocity of the two objects, assuming
masses remain constant:
e = (vf1 – vf2) / (vi1 – vi2)
Where vf2 and vf1 are velocities after impact,
and vi1 and vi2 are velocities before impact.
12B-11
Angle of Rebound
 For a perfectly elastic object, the angle of incidence
(striking) is equal to the angle of reflection
(rebound).
 As coefficient of elasticity changes variations will
occur.
Fig 12.22
12B-12
Effects of Spin on Bounce
 A ball with topspin will rebound from horizontal
surface lower and with more horizontal velocity.
 A ball with backspin will rebound higher and with less
horizontal velocity.
 A ball with no spin will develop topspin.
 A ball with topspin will gain more topspin.
 A ball with backspin may be stopped or reversed.
 Spinning balls hitting vertical surfaces will react in
the same manner as with horizontal surfaces, but in
relation to the vertical surface.
12B-13
Fluid Forces
 Water and air are both fluids and as such
are subject to many of the same laws and
principles.
 The fluid forces of buoyancy, drag, and lift
apply in both mediums and have
considerable effect on the movements of
the human body.
12B-14
Buoyancy
 Archimedes’ Principle: a body immersed in a
liquid is buoyed up by a force equal to the
weight of the liquid displaced.
 This explains why some things float and
some things sink.
 Density is a ratio of the weight of an object
to its volume.
12B-15
Specific gravity
 Ratio of the density of an object to the
density of water.
 An object the same weight for volume as
water has a specific gravity of 1.0.
 An object with specific gravity > 1.0 will sink.
 An object with specific gravity < 1.0 will float.
12B-16
Lift and Drag
Drag is the resistance to
forward motion through a
fluid.
Result of :
 fluid pressure on the leading
edge of the object.
 amount of backward pull
produced by turbulence on
the trailing edge.
Fig 12.24 b
12B-17
Lift and Drag
Laminar flow is a smooth, unbroken flow of fluid
around an object.
 A smooth surface will have better laminar flow
than a rough surface, resulting in less drag.
Fig 12.24 a
12B-18
Lift and Drag
Lift is the result of changes in fluid pressure as
the result of difference in air flow velocities.
Bernoulli’s Principle: the pressure in a moving
fluid decreases as the speed increases.
V P
Fig 12.24 c
Lift
Drag
V P
12B-19
Ball Spin (Magnus Effect)
 Bernoulli’s Principle
applies here also.
 A ball will move in the
direction of least air
pressure.
 A ball spinning drags a
boundary layer of air
with it, causing air to
move faster & reducing
pressure on one side.
Fig 12.25
12B-20
Free Body Diagrams
 In analyzing any technique, one should consider
all external forces, by accounting for the effect
of each one on the body.
 The isolated body is considered a separate
mechanical system.
 Easier to identify forces & represent as vectors.
 Can help determine the application and direction
of forces acting on the body.
12B-21
Direction & Point of Application of
External Forces
Force
Direction of Force
Point of Application
Weight (W)
Downward
Center of Gravity
Normal (R)
Perpendicular
Point of contact
Friction (F)
Along surface
Point of Contact
Buoyancy
(B)
Upward
Center of buoyancy
Drag (D)
Opposite flow
Center of Gravity
Lift (L)
Perpendicular to drag Center of Gravity
12B-22
Free Body Diagram
 Magnitude
 arrow length
 Direction
 arrow head
 Point of application
 arrow tail
 Weight (W)
 Reactive force (R)
 Friction (F)
Fig 12.26
12B-23
Free Body Diagram
 Also used to show forces
on a body segment.
 Thigh is isolated:
 Weight of thigh (W)
 Muscle force Hip (MH)
 Reactive Forces
 Hip (Hx & Hy)
 Knee (Kx & Ky))
Fig 12.28
12B-24
Work, Power, and Energy
Work
 Work is the product of force expended and
the distance over which force is applied.
W = Fs
 Work (W), Force (F), Distance (s)
 Units are any combination of force &
distance:
 foot/pounds,
 joule = 107 x 1 gram / 1 centimeter
12B-25
Work
 A 20 N suitcase is place on a shelf 2 m above
the ground:
 Work done against gravity= 40 Nm
 Same suitcase lifted along a 4 m incline is still
40 Nm of work against gravity.
 Horizontal distance not included.
4m
2m
30o
12B-26
Positive & Negative Work
 Positive work – force acts in the same
direction as that of the objects
motion.
 Negative work – force acts in the
direction opposite to that of the
objects motion.
12B-27
Mechanical Muscular Work
Example: a rectangular muscle 10 cm x 3 cm,
that exerts 240 N of force.
 Average muscle fiber shortens 1/2 its length.
W = Fs
W = 240 N x 5 cm
W = 1200 N•cm or 120 Nm
12B-28
Force per Muscle Cross Section
 If force of the muscle is not known, it is computed
from the muscle’s cross section.
Example: Assume same muscle is 1cm thick:
Cross section = width x thickness
3 cm X 1 cm = 3 sq cm
Average force = 360 N per sq cm
F = 360 x 3 = 1080 N
W = Fs
W = 1080 N x 5 cm = 5400 N cm or 540 Nm
12B-29
Muscular Work
 If the internal structure of the muscle is
rectangular, a simple geometric cross-sectional
measure can be used.
 For penniform & bipenniform muscle,
physiological cross section must be
determined.
 “s” represents 1/2 the length of the average
fiber.
 Force per square inch depends on whose
research the student accepts.
12B-30
Muscle Work by
Physiological Cross Section (PCS)
W = Average force x PCS (sq cm) x .5 length of
fibers (cm)
Divide by 100 to convert N-cm to Nm
W (Nm) = 360 x PCS (sq cm) x .5 fiber length (cm)
100
12B-31
Power
 The rate at which work is done.
P = Fs / t or P = W / t or
P = Fv
P = Power
t = time
W = work
v = velocity = s / t
12B-32
Energy
 The capacity to do work.
Law of Conservation of Energy:
The total amount of energy possessed by a
body or an isolated system remains
constant.
12B-33
Potential Energy
 Potential energy: energy based on position.
 Potential energy is the product of the
weight of an object and the distance over
which it can act:
PE = mgh
m = mass, g = gravity, h = height
12B-34
Kinetic Energy
Energy based on motion:
KE =
1/2
mv2
m = mass, v = velocity
Work done is equal to the kinetic
energy acquired, or
Fs =
1/2
mv2
12B-35
Analysis of Linear Motion
First identify the nature of the
forces involved in the motion of
interest:
 Weight
 Propulsive forces
 Ground Reaction Force
 Friction
 Buoyancy, Drag, & Lift
12B-36
Analysis of Linear Motion
 The principles that govern the mechanical
aspects of a movement can be summarized
by examining some of the basic concepts
involved in the kinetics of linear motion:
 Inertia
 Impulse
 Work & Power
 Potential & Kinetic Energy
12B-37